The foot-mouths are odd enough and integral enough that I think they would have had to be a pretty original mechanism in Andalite evolution. My guess is that they started with at least one mammalian proboscis that also functioned as a leg. Perhaps as they developed either in size or intelligence some mutation occurred that caused this proboscis to take the place of four of their legs rather than just one, to meet increasing nutritional needs.
Alternatively (and to explain the hands) rather than merely "replacing" the legs with the proboscises it became evolutionarily advantageous to evolve more, and at some point the proto-andalites had both multiple mouth-legs and multiple normal-legs. Once this form was established, it became more natural for the grazers to simply walk on their proboscises all the time, leaving the original legs redundant. This freed the original limbs to perform other tasks; I imagine that prior to the introduction of thought-speak by Toomin, they may have communicated mostly through hand-signals. Their intellect may have developed concurrently with their hands, as those who could communicate by waving their redundant limbs survived longer than those who couldn't. The ability to make more complex hand signals developed concurrently with the ability to understand them and so on, until we found something resembling the seven-fingered hands of the Andalites. These would be altered even further as Andalite intellect developed and those who could use their communicative-limbs to manipulate their environment out-survived those that couldn't, and the hands became more and more developed to facilitate tool-use. However, since (evolutionarily) this is a secondary purpose for the Andalite's hands, they remain relatively weak. After all, the Andalites were morphologically complete by the time that thought-speech was invented, meaning that natural selection still favored those whose hands were dexterous and communicative over those whose hands were strong and manipulative.
Likewise, their third redundant limb (most logically a rear limb; in the original set-up, we can presume that the proboscis was one of the back legs, with the two front legs becoming the arms after the "proboscis expansion" and with the other former back leg sticking out in the manner I am about to describe) would have been of limited use developing enhanced dexterity or appendages, due to its comparative distance and thus the difficulty of discerning its finer movements. Instead, evolution would have favored a limb capable of a wider degree of gross movement, a more flexible limb similar in fashion to the Andalite tails we see today. From there, it's sensible to suppose that (being a prey-species) those Andalites who developed deadly weapons at the end of these flexible and increasingly long limbs would have lasted longer and been selected for.
The proboscises would have developed hooves later in their existence as they were relied on more as feet. This likely would have resembled standard hoof-development, though obviously they must have developed so as to keep the food path open (though likely collapsible!) Perhaps the hooves feature some sort of natural "hinge" allowing them to open to accept food.
What we have so far is a creature featuring all of the limbs typical of the Andalites. Other Andalite features may have developed at any other time during this process. The multiple Andalite hearts are of obvious value to a species of such size and activity, allowing them to supply all parts of the body with blood even at peak-physical performance. Stalk-eyes are of obvious value to the Andalites as a prey-species, and their high positioning would have allowed them to detect a variety of threats in their native grassy terrain. Since it would be odd for a pair of stalk-eyes to develop in the middle of an already-developed skull, chances are the Andalites had four eyes to begin with, and over time two of them protruded farther and farther from the face, eventually taking their form and position on the skull. It may even be that they originally developed with eyes literally on the backs of their heads, and that 360 degree vision is a trait their brains are long-accustomed to.
The Andalites' sense of smell is clearly not meant to discern quality or variation in their food, given their almost non-existent (but still present, see: Elfangor's reference to "flavors of grass") sense of taste. Given the positioning of their noses (high up on the body rather than low on the ground near their food), they likely function to detect pheremones (which would have been useful for communication) and perhaps the scents of predators.
Finally, the fur of the Andalites has historically ranged from blue to purple with tan stripes. Given that this coloration varies depending upon sex and age, its function seems to be for sexual selection rather than camouflage, with the vibrancy of one's coat indicating one's health, vigor and probable status within the community.